Each column represents a sample from a different population. For each column, id

Question

Each column represents a sample from a different population. For each column, identify a probability distribution that is consistent with that sample. You must include the values for all necessary parameters for the distribution you propose (e.g. µ, , , , a, b, , etc. as appropriate).

5.600688 -12.7611 12.34117 0.182076 43.40935 -10.9186 17.64488 0.133441 8.94086 -13.4035 24.47454 0.050684 29.00289 -10.193 22.0102 0.217709 34.29425 -11.1426 19.65623 0.204923 2.061524 -10.4194 13.4902 0.03368 43.36892 -12.7662 17.87845 0.18669 -33.6541 -7.6221 28.22186 0.195953 -7.26863 -10.7319 28.06807 0.152912 38.72871 -6.01332 25.94807 0.19103 30.14037 -9.08829 19.86072 0.024289 -14.6024 -9.05736 17.03345 0.265362 16.05463 -9.36813 14.99188 0.349845 -18.5804 -10.6398 20.56887 0.21996 48.43019 -11.2619 18.892 0.029613 -1.39894 -10.556 15.27679 0.121233 33.12034 -15.07 23.70861 0.309468 -15.6408 -12.9132 14.55641 0.10917 -38.7986 -8.47424 15.62737 0.275158 -17.5833 -9.3954 19.72859 0.175303 -36.9499 -11.1898 19.23862 0.04608 -39.2253 -7.28271 19.26556 0.215305 -13.286 -9.7132 31.12595 0.23024 39.55181 -9.64505 13.53789 0.048752 1.322895 -10.7783 17.21491 0.18113 0.828855 -10.2089 23.36966 0.390804 12.15356 -10.8288 21.02348 0.071765 10.19957 -10.4949 20.25265 0.331207 -42.9983 -12.7005 10.66121 0.107322 10.77696 -9.07893 17.69825 0.30299 23.80946 -7.54331 22.92917 0.096693 44.63813 -9.54716 20.5839 0.308296 -15.8468 -8.31897 25.03617 0.374974 -25.9513 -8.41949 19.6038 0.048968 12.5502 -7.67425 13.46088 0.245007 -4.27205 -10.2609 14.31816 0.085735 47.01118 -13.4571 22.29471 0.073927 7.678165 -9.02657 13.98484 0.58872 41.01337 -11.4061 12.75863 0.258219 43.43697 -10.0733 27.02613 0.236855 5.157 -9.86947 25.42222 0.269702 4.004489 -13.5685 31.25429 0.269877 -20.747 -10.5877 13.40112 0.129578 42.89019 -12.5722 11.19468 0.250133 -11.0056 -11.115 27.01773 0.249574 24.2535 -9.95404 24.85642 0.06431 -9.16511 -8.60989 16.16749 0.269382 10.90937 -10.4648 17.95233 0.075476 11.38937 -5.54802 20.24754 0.074122 23.52837 -8.28576 13.19996 0.053715 -8.11169 -9.47905 12.21586 0.062169 -46.6917 -13.23 23.39243 0.246205 -9.99947 -5.90146 10.63921 0.079176 -47.3573 -8.81688 14.72393 0.155844 28.16413 -11.0574 12.32085 0.396434 -8.95182 -11.1063 33.48162 0.295025 19.55066 -7.26682 19.38514 0.0289 -46.7674 -8.44602 17.63094 0.104579 5.747652 -10.0303 22.10645 0.138663 30.07509 -10.577 23.5998 0.281953 4.009713 -10.7384 14.36968 0.133885 23.28015 -11.1922 19.86411 0.13136 -1.89981 -11.6217 26.13256 0.350535 44.54959 -10.0179 15.82301 0.280674 30.29808 -8.29882 9.708756 0.202531 22.92735 -11.819 31.76407 0.521042 31.3597 -9.40103 17.17045 0.083237 -38.7136 -10.5225 14.15892 0.040094 -24.4854 -9.33806 22.49595 0.082138 17.21638 -12.2521 21.98269 0.142036 3.965037 -10.1739 17.99059 0.071602 -27.1413 -8.76218 16.78703 0.287133 48.0894 -11.6599 26.64706 0.327586 16.13055 -9.15553 19.82826 0.150687 44.52363 -9.96897 22.99297 0.060221 -11.7241 -7.65515 30.28319 0.405784 32.59147 -10.1838 11.79626 0.223299 8.834689 -11.3564 21.858 0.307889 34.8103 -10.3973 13.6525 0.224341 -47.0283 -13.3194 13.80878 0.205192 -11.1351 -8.9261 18.91157 0.14378 13.51879 -7.00584 16.31737 0.055559 13.74334 -9.08198 18.47847 0.219028 39.95831 -10.712 19.21295 0.104467 -43.9979 -7.3606 29.33163 0.087075 21.71761 -7.95084 11.70101 0.364682 44.27367 -10.427 18.22496 0.200989 10.79272 -10.7193 16.42624 0.074435 -49.5079 -8.25991 14.42154 0.024912 29.01922 -10.0581 27.10558 0.166555 -48.7507 -10.3642 19.81869 0.167019 -9.38364 -9.98585 11.95826 0.13106 -16.5685 -10.4676 27.73239 0.144426 -28.2522 -11.0135 22.07801 0.061774 -36.2892 -9.16977 24.3155 0.241133 44.12088 -10.1676 25.46476 0.2743 -3.12466 -10.6672 16.23506 0.111168 -9.39244 -8.22437 10.65086 0.020534 5.687402 -6.23367 26.32344 0.046026 0.524749 -10.4192 22.95921 0.171385

Explanation / Answer

1)

To identify the distribution, we use Stat > Quality Tools > Individual Distribution Identification in Minitab.

We select whose p-value is higher ,

We have chosen C2,C3 as well as C4

C2      Logistic

Location                               scale   

µ = -10.02255            s = 0.99285

C3 follow Lognormal distribution

Location                          scale

µ = 2.93000        = 0.29300

C4 follow Weibull distribution

Shape                scale

K = 1.63724     = 0.20379

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